On the Tensile and Compressive Strength of Solids Weakened (Strengthened) by an Inhomogeneity

By considering the stress interaction between an inhomogeneity embedded in an elastic brittle-like solid and the preexisting microcracks (“Griffith cracks”) inherent to the solid, several puzzling phenomena concerning the apparent anomalous “size effect” on the fracture strength of solids weakened (strengthened) by a cutout (reinforcement) are explained quantitatively. The various conditions under which a cylindrical inhomogeneity in an otherwise homogeneous body enhances the strength of the body or weakens it when the body is subjected to load normal to the cylindrical axis are revealed and discussed. In particular it is shown that uniaxial tensile and compressive critical loads required to fracture material with various hole sizes are predictable as confirmed by experiments with quasi-isotropic composite materials, rocks, and high strength alloys found in the open literature. The entries to these predictive functions are the two independent fracture properties of the material; tensile strength and toughness of the virgin material, or the typical size of the Griffith cracks. As a by-product, the extremely high compressive strength of a material (with respect to its tensile strength) with vanishingly small inhomogeneity emerges.